A minaret at sunrise and the soft lament of a Muslim call to prayer. Nobody needs to wait for a location — Damascus, Baghdad, Tehran — to be tapped out in military-style type.

That image has become as common and convenient a signifier as helicopters flying over rice paddies to the sounds of Buffalo Springfield (“Stop, children, what’s that sound? Everybody look what’s going down”) are for the Vietnam War.

If a show opens with a mosque bathed in dim light and mournful Middle Eastern music, then this must be a drama about Washington and the war on terrorism.

That’s how “Madam Secretary” begins on Sunday on CBS, and that familiar landscape (in this case, it’s Damascus at dawn) is an early clue that there is not a lot of creative license in this enjoyable but by-the-book drama about a female secretary of state.

Hillary Rodham Clinton is the obvious inspiration, but this is Hillary with a human face: Téa Leoni, who has a husky voice and a loose, engaging manner, is an unusually likable beauty. As Elizabeth McCord, she has all the brains and determination of the original and none of the political ambition and baggage.

It’s a what-if scenario, a wish-fulfillment do-over in which Mrs. Clinton is dragged reluctantly into high office and spends her time there making the world a safer place, not planning her next move in Iowa.

And that’s why a closer model for Mrs. Clinton can be found in a different what-if scenario, namely that of “The Good Wife,” the series about a politician’s wife whose husband is brought down by a sex scandal. She stands by his side for a while, then leaves him and restarts her legal career from scratch.

That CBS drama returns for a sixth season on Sunday, and the premiere is bracing and unexpected. Especially given how long this show has lasted, it’s a credit to the imagination and energy of its married creators, Robert and Michelle King, that “The Good Wife” has remained so watchable.

But another reason for its enduring popularity is that Alicia Florrick, the betrayed wife played by Julianna Margulies, has guile as well as gumption. She is sympathetic but also devious and not beyond using connections, deceiving friends and twisting the truth to get what she wants, including, last season, her own firm.

In other words, Alicia is a closer match to Mrs. Clinton: believably imperfect even when legal plot twists grow convoluted and outré.

In some ways, “Madam Secretary” seeks to be realistic about Washington. The first episode involves hostage taking in Syria and even a failed rescue operation that eerily echoes the one that the Obama administration ordered over the summer to save James Foley and other Americans held by the group that calls itself the Islamic State, even though the pilot was filmed before revelations of the government attempt.

This is a prime-time network show, however, so the outcome is not as horrible as the videotaped beheadings that happened in real life.

The presentation of politics is just as sanitized. In this fantasy, Elizabeth did not seek a cabinet post; it was forced upon her. She is a former C.I.A. analyst who quit for unexplained ethical reasons and is content to teach political science and raise horses with her husband, Henry (Tim Daly), and their two children. Elizabeth reluctantly accepts the job only after the president (Keith Carradine), her former mentor at the C.I.A., insists.

She arrives in Washington, ready to make a difference and immediately gets on the wrong side of the president’s domineering and manipulative chief of staff, Russell Jackson, who so resembles former Vice President Dick Cheney that the actor, Zeljko Ivanek, sports a ghost of the crooked half-smile that Mr. Cheney was famous for.

Russell wants to be in charge. Elizabeth wants to save lives. In one of the show’s better scenes, Russell confronts Elizabeth after she handled a crisis without his approval. He asks her how she did it.

Television is suddenly full of women in power, and that is as much because of Shonda Rhimes and the success of her Washington melodrama, “Scandal,” as because of Mrs. Clinton. “Homeland,” the Showtime espionage thriller, has also opened doors.

“State of Affairs,” an NBC show coming in November, doubles down by stealing a bit from “Scandal” and a bit from “Homeland.” Alfre Woodard is the president, and Katherine Heigl is her most trusted, though personally troubled, national security adviser.

Oddly, these new dramas showcase bold women in command but are timid about tapping into the kind of cynicism and character assassination that helped “Scandal” and “House of Cards,” on Netflix, become hits.

ABC had enough faith in Ms. Rhimes, after her “Grey’s Anatomy” proved a hit, to back “Scandal” and won big. CBS, which has had so much success with squeaky-clean naval heroes on “NCIS” that it is adding a second spinoff, “NCIS: New Orleans,” on Tuesday, is evidently loath to try material that may be too dark for many viewers.

“The Good Wife” stands out because it strikes the right balance of network-mandated virtue and cable-inspired vice. “Madam Secretary” has some good moments, but it would be better if its heroine were just a little bit worse.